Since stumbling upon it in 5th grade channel surfing one Sunday morning, I was an avid regular watcher of the cartoon as a kid.
Just as Robert Altman films and ensemble shows optimize your attention span by dividing it among multiple storylines, I liked how the X-Men delved into relatively interesting characters and then threw different side and recurring characters into the mix as the universe expanded. We're usually slow to recognize just how drawn in we are to action scenes and the X-Men had action scenes that involved the laws of science and so much more creativity. The way each person had different powers and they would neutralize each other in different ways made it more like chess.
That gush of anticipation that every fanboy feels when something they've embraced only in the often-lonely medium of comics becomes translated to the screen when all those comic books were turned into event films. I only felt that once with X-Men and I wasn't disappointed (with the exception that many of the characters from the cartoon weren't in the film) because the action scenes and production values were great. But most importantly, the film had such pitch-perfect casting. Halle Berry's only memorably piece of work outside of Monster's Ball to justify her Oscar was in the X-Men trilogy, a role which got better and more weighty with each picture. Hugh Jackman has made himself a star worthy of working with the industry's best directors out of Wolverine and deservedly so.
The downside of seeing these cartoons fully-realized on a live movie screen in such a satisfying way is that in retrospect the cartoon looks ridiculous. Of course, our standards of quality tend to change massively with age to the point where things we liked as kids don't hold up as adults. This is no exception.
Just watch the first minute and a half of this clip and cringe with me at its ridiculousness:
The action is accompanied by bad puns at a rate of something like 3.5 per minute. It's as if there's a rulebook in the X-Men training manual that says you have to accompany every time you use your powers with some sort of trash talking.
Also, look at the differences between the cartoons and their on-screen counterparts:
1. Storm had a hint of sexiness to her and she was grounded in a mix of idealism (i.e. the scene in X3 where she discourages Rogue from thinking of being a mutant as a disease) and world-weariness (i.e. having to turn Angel away from protection of a life as a mutant for no reason other than she can't handle the demands). In the cartoon, there's none of these shades of gray as Storm sounds as authoritative as Charlton Heston from the Ten Commandments.
2. Wolverine is defined by his raspy voice which his shows his cheerlessness and tough-as-nails persona from a scrappy existence. However, in the film, Jackman is capable of convincingly portraying a whole range of emotions underneath.
3. Maybe it was because the cartoon's writing staff were comic book scribes for whom portraying the subtleties of romance wasn't a forte, but Jean Grey was nothing more than arm candy for Cyclops. The writing staff said in an interview that the love triangle between Cyclops, Jean and Wolverine was the thing they were most proud of. What love triangle?! When Jean was so lovey-dovey with Cyclops in the cartoon, who would have thought that Wolverine had a chance?
With Famke Janssen's wonderful portrayal of Jean Grey, she's much more enigmatic in her affections driving the love triangle along much better. She's also a more empowered woman: The first time we see her on-screen she's referred to as Dr. Jean Grey. In her second appearance on screen, she's actually shown doctoring.
On the other hand, the cartoon versions of Beast, Professor X, and Cyclops are all more or less adequate in comparison to their movie parts. James Marsden, for example, didn't have much of a presence in the film and neither does the cartoon version, so it's essentially a tie. It's not entirely Marsden's fault: Since the movies are Wolverine-centric that makes Cyclops the douche who the hero's love interest is currently attached to, and that makes it beneficial that Cyclops is played by a professional schlub.
Beast can get annoying in the cartoon because the writers try too hard to make him sound intellectual, but he doesn't change that much in the film. He still quotes famous intellectuals during fight scenes but in far reduced frequency (he only has one fight scene) and he's equally as snobby in the film but there's more of a use for it as he's made a cabinet official.
Bottom line: There are some children's series that are well-done enough that you enjoy them as adults like Pinky and the Brain, Animaniacs or Looney Tunes. X-Men, unfortunately, isn't one of them.
Here's a 4-part retrospective I just read on the topic: